Transient response of asymmetric bistable piezoelectric oscillators under-Gaussian white-noise excitation using a Gaussian basis-function method

Bistable piezoelectric transducers can capture a broad range of vibration frequencies. They respond to weak excitations and deliver high energy density. These features make them useful for microscale energy harvesting and sensitive detection. This paper considers an asymmetric double-well piezoelectric oscillator subjected to Gaussian white noise. We derive a dimensionless model under open-circuit conditions and then propose a solver for the transient Fokker–Planck–Kolmogorov equation using a Gaussian basis function expansion. The scheme uses explicit time stepping and a regularized projection correction. With probability normalization enforced at every step, it yields the transient probability density function evolution. Monte Carlo simulations confirm the method's accuracy across the tested cases. We consider the method reliable for assessing dynamic reliability and optimizing performance in bistable devices.